System for determining a useful life of core deposits and interest rate sensitivity thereof

ABSTRACT

A method and system for determining a useful life of financial instruments, such as financial assets and liabilities. A dynamic calculation of a first retention rate is performed for each of several financial assets; a steady-state calculation of a second retention rate is performed for the financial assets; and the first and second retention rates are combined to determine a predicted useful life of the combined financial assets. 
     Optionally, one of several variables affecting at least one of the retention rates is selected. A sensitivity of financial asset variables to other financial asset variables is determined. Scenarios are forecast, extrapolated from the retention rate. The financial assets may include deposits and/or financial instruments. Outliers in the financial assets may be checked, in one variation of the invention. Exogenous variables may be included in at least one of the calculations. The exogenous variables are selected from the set including seasonal variables, day-of-the-month variables, treasury interest rates, deposit rates, local unemployment rate, local personal income, and local retail sales, and the like. Interest rate spread may be included in at least one of the calculations. Forecast scenarios may include future values for use in at least one of the calculations. The future values may be selected from the set including forecast treasure rates, forecast horizon, forecast deposits, forecast retention rates, and forecast interest rates, and the like.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention generally relates to financial forecasting and planning.More particularly, it concerns estimating the expected life of deposits,especially core deposits (a/k/a non-maturity deposits), at a financialinstitution, to ascertain the sensitivity of deposits to changes invariables determined outside the financial institution such as interestrate changes, and to forecast the behavior of deposits.

2. Description of the Related Art

Financial institutions take in different types of deposits and payinterest on those deposits while simultaneously purchasing assets andreceiving interest on those assets. The profitability of a financialinstitution depends on its ability to earn higher interest rates on itsassets than it pays for its deposits.

Generally, the longer the maturity of an asset the higher the interestrate paid on it. This creates a performance incentive for financialinstitution managers to buy longer maturity assets. Funding longermaturity assets with retail deposits presents special challenges,though. This is because balances in some types of deposits—so called“core deposits” (a/k/a non-maturity deposits) including categories suchas NOW (Negotiable Order of Withdrawal), savings, checking and MMDA(money market demand accounts), are eligible to be withdrawn from theinstitution actually or virtually upon demand. If such deposits are usedto buy longer maturity assets, a potentially serious asset and liabilitymaturity mis-match is apparently created.

In fact, however, a substantial fraction of core deposits tend to stayin an institution for a period measured in years rather than in days orweeks. Thus, financial institutions can and do in a probabilistic senseuse these deposits to fund purchases of long-term assets. However, suchpurchases are fraught with uncertainty given the unknown true maturityof the underlying deposits.

There have been three major types of efforts aimed at resolving theproblem of determining the expected life of core deposits as well asnumerous attempts to address parts of the problem. Possibly the earliestefforts involve regulators including the Office of Thrift Supervision(OTS), the Office of the Comptroller of the Currency (OCC) and theFederal Reserve (Fed). All these regulatory bodies have, at least inpart in the interests of simplicity and fairness, adopted a “one sizefits all” approach to considering the probabilistic withdrawal of coredeposits.

The Fed has made its conclusions the most explicit of the three. Forexample, see David M. Wright and James V. Houpt, “An Analysis ofCommercial Bank Exposure to Interest Rate Risk,” Federal ReserveBulletin, (February 1996, pp. 115-28).

In contrast, the OTS has been the most secretive about its internalprocess which is essentially a black box to those outside the OTS,although notes released and Fed publications indicate that OTS and Fedprocedures are very similar. The Fed's published work indicates that ithas examined a cross-section of financial institutions and has estimatedthe average lives of all types of core deposits to be very short,typically less than five years, with checking accounts in particularhaving a life of approximately one year.

There are two problems with the approach of these regulatory bodies.First, they have been exceptionally conservative in their estimates ofdeposit lives, a finding not the least surprising given their regulatoryroles. Setting short lives for core deposits increases the probabilitythat a financial institution will not experience financial distress fromexcessive asset-liability maturity mismatch and thus cause problems forthe regulator. The fact that this constraint may have major implicationsfor profitability is not typically considered. Second, they have set anaverage life for a particular type of core deposit that does not varyacross institutions. This unfortunately fails to address the issue thatthe different clienteles served in, say, a retirement community inFlorida versus a suburb of Las Vegas, might cause dramatic differencesin the behavior of deposits in those different local institutions.

The second general type of effort has been in the academic literature.An article by Richard G. Anderson, E. Jayne McCarthy and Leslie A.Patten, “Valuing the Core Deposits of Financial Institutions: AStatistical Analysis” in the Journal of Bank Research (vol. 17 #1, 1986,pp. 9-17) is perhaps the most complete and explicit statement of theprocess. Anderson et al. proposes sampling accounts at one institutionon a yearly basis and then calculating what fraction of accounts remainwith the institution from one to fifteen years later. The results inpart address one limitation of the regulators' approach in that theyconsider only one institution rather than taking a cross-section ofinstitutions at a point in time. The approach is to sample accounts atyear-end and then consider the percentage of accounts remaining with theinstitution at year-end in subsequent years. The ratio of accounts (byaccount age) and the retention rate of accounts are calculated. Thisretention rate is then employed to estimate the economic value of thecore accounts.

Nevertheless, this account sampling approach fails in at least twodimensions. First, it considers the number of accounts rather than thevolume of funds in accounts. If larger accounts tend to remain with aninstitution while small accounts are more likely to be closed, thisapproach would seriously understate the value of a $1 in deposits.Second, there is no attempt to relate the retention rate to economicconditions, including interest rates or interest rate spreads. Andersonet al. fail to consider that both the number of accounts and the totalbalances of those accounts are related to interest rate differentials.For example, Anderson et al. do not take into account that, as aninstitution raises its rate relative to market rates, there might be ahigher retention rate for deposits in retained accounts.

The third type of effort has been in the consulting area and isprincipally expressed in two publications. The first is by Z.Christopher Mercer, Valuing Financial Institutions (Homewood, Ill:Business One Irwin, 1992). In Chapter 19, “Branch Valuations and CoreDeposit Appraisals,” Mercer presents what is likely the most explicitstatement of the process of valuing core deposits. (In particular,consider Exhibits 19-3 through 19-8.) The methodology, however, isfundamentally the same as that in Anderson, et al. mentioned above andis subject to the same limitations.

The other statement of approach, labeled the Commerce Methodology, isbriefly described in the American Banker, (May 3, 1996), N.J.'s CommerceUsing High-Power Method to Evaluate Deposits and examined in more detailin Chapters 7 and 8 of Interest Rate Risk Models: Theory and Practice,by Anthony Cornyn and Elizabeth Mays (Editors), Glenlake Publishers,Chicago, London, New Dehli: 1997. That approach, developed by William J.McGuire and Richard G. Sheehan, the inventors, rectifies many of thedifficulties with the approaches mentioned above. There initially is asurvey of deposits, as with Anderson, et al. and Mercer, and that surveyfocuses on the total balances in the survey accounts. Those balances arethen related to market rates including Treasury rates using regressionanalysis. The regressions yield simple linear relations between Treasuryrates and prior retention rates. These linear relations then areemployed to forecast retention rates for any time horizon and serve asthe basis for valuing core deposits. The Commerce Methodology representsa dramatic improvement over all prior methodologies and has beensubsequently employed for a number of financial institutions.

However, even the Commerce Methodology has limitations, in particularconcerning the statistical specifications implicit in the methodology.That is, when retention rates are linked to other variables includingTreasury rates, there remains a question concerning exactly whichvariables are to be included in the equation and how sensitive theresults are to the particular equation employed or to the particularregression estimated. In addition, as with all conventionalmethodologies, the process of calculating the forecasted retention ratesand their values is potentially dependent on the last few observationsin the sample. That is, deposits are sampled monthly and if the lastmonth indicates a sharp downturn in deposits, even though there may havebeen limited declines elsewhere in, say, a 48 month sample, the forecastmay place more emphasis on that last month and to project that such adecline will become the norm in the forecasted period. The CommerceMethodology also has the deficiency as with prior methodologies that itrestricts the relationships between variables influencing retentionrates to be linear. There is no reason, however, why Treasury ratechanges, for example, would necessarily influence a financialinstitution's deposits in a strict linear fashion. Finally, the CommerceMethodology does not allow asymmetries in relationships. That is, anincrease in deposit rates and a decrease in deposit rates are treated asthough they have the same impact (with the sign reversed) on the levelof deposits. That procedure does not accommodate a case such as when adepositor may choose to keep deposits in an institution with a rateincrease but may choose to leave with a rate decrease, for example.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a system that moreaccurately determines the expected lifetime and the expected value of afinancial institution's core deposits. It is another object of thepresent invention to allow financial institutions greater flexibility inthe assets purchased using core deposits, possibly funding purchases oflonger term and higher yield assets.

Another object of the invention is to provide a system to determine theinterest rate sensitivity of core deposits. Another object of theinvention is to allow a financial institution to predict how interestrate changes will influence core deposits' expected lifetime and thisvalue to the institution.

Another object of the invention is to precisely and accurately forecastthe retention rates of core deposits, the financial institution'sinterest rates, and the financial institution's total deposit balancesall in the context of a single unified model.

Another object is to provide a method of forecasting the expected lifeof core deposits, thereby to allow the financial institution to obtainthe correct—and in many cases likely the longest possible—assets tomatch with the deposit base.

Another object is as factors such as interest rates change, to forecasthow deposits will change, thereby to permit the financial institution todetermine how much risk to accept by stretching—or not stretching—thelives of assets.

In accordance with these and other objects, there is provided a methodand system for determining a useful life of financial assets. In acomputerized system, a dynamic calculation of a first retention rate isperformed for each of several financial assets. In the computerizedsystem, a steady-state calculation of a second retention rate isperformed for the financial assets. The first and second retention ratesare combined to determine a predicted useful life of the combinedfinancial assets.

The following are included in preferred embodiments of the invention.Optionally, one of several variables affecting at least one of theretention rates is selected. A sensitivity of financial asset variablesto other financial asset variables is determined. Scenarios areforecast, extrapolated from the retention rate.

In preferred embodiments, the financial assets include deposits and/orfinancial instruments. Data for each of the financial assets includestotal deposit balances, deposit rates, and a sample of account balances.Data may be received for each of a the several financial assets. Alength of the sample may be about four years. In highly preferredembodiments, the size of the sample may be n=4k²s²/d², and wherein s isan estimated yearly retention rate, d is about in the range of 0.01 to0.03, and k is a level of significance of about 1.96. Most preferably, dof about 0.03 is used for hand-collected, and 0.01 or 0.015 is used forelectronic.

Outliers in the financial assets may be checked, in one variation of theinvention.

In further variations of the invention, exogenous variables may beincluded in at least one of the calculations. The exogenous variablesare selected from the set including seasonal variables, day-of-the-monthvariables, treasury interest rates, deposit rates, local unemploymentrate, local personal income, and local retail sales, and the like.

In another variation of the invention, interest rate spread may beincluded in at least one of the calculations.

In yet another embodiment, forecast scenarios may include future valuesfor use in at least one of the calculations. The future values may beselected from the set including forecast treasure rates, forecasthorizon, forecast deposits, forecast retention rates, and forecastinterest rates, and the like.

In another embodiment, the predicted useful life of the combinedfinancial assets may be output, such as on a display.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in connection with the drawings.

FIG. 1 is a block diagram illustrating data assembly.

FIG. 2 is a flow chart illustrating basic estimation.

FIG. 3 is a flow chart illustrating estimation alternatives.

FIG. 4 is a flow chart illustrating forecasting procedure.

FIG. 5 is a production schematic of MPS core deposits and CD behaviorreports.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The invention will be described herein in five parts for ease ofunderstanding, without limitation. The first consists of a process forcapturing or receiving initial data from a financial institution andputting the initial data in a predetermined format for use in subsequentprocesses. The second involves a process for selection of variables thatinfluence retention rates in particular as well as total depositbalances and the institution's interest rates. The third involvesalternatives allowed to the basic process described in the second part.That is, there is a basic approach to the estimation process but thereare a number of alternatives that a financial institution can choosedepending on the use of the forecasts. The fourth part is the actualforecasting process itself which is based on the estimation described insteps two and three. The forecasting process also allows an institutiona number of alternatives depending on the use of the forecasts. Finally,the fifth step involves taking the results from the forecasting equationand using them in particular business applications, in particular,calculating the value of core deposits and their sensitivity to factorssuch as interest rate changes. The rest of this section describes eachof these parts in more detail.

Part One

Reference is made to FIG. 1. Data is obtained from a financialinstitution, typically on three types of variables: (1) theinstitution's total deposit balances by type of deposit for a varyingnumber of categories of deposits 107, (2) the institution's depositrates 109, also by type of deposit for a varying number of categories ofrates, and (3) a sample of the institution's individual accounts 103,again by type of deposit for a varying number of categories of accounts.Typically the data is on a monthly basis and will be referred tohereafter as monthly although the general process can be employed ondifferent frequency data, including quarterly, weekly or bi-weekly. Thedata on the institution's total balances and deposit rates typically donot need—should not need—further adjustment unless different depositcategories are being combined. (That is, the aggregate values are notmodified unless the institution needs to combine multiple categories ofdeposits, for example, regular MMDA deposits and higher-yield MMDAdeposits.) The sample of individual accounts, however, often requiresadditional detail presented below.

A survey sample size is determined 101. On the appropriate length of thedata sample, there is no hard statistical rule on what sample timeperiod (length) would be required. The process preferably employs aminimum of four years of monthly data for a minimum of 48 observations.This sample length provides enough information typically to obtainreasonable estimates and forecasts, although longer data samples aredesired when available. (The maximum useful length of the data samplegenerally would be no more than ten years. Longer samples would beproblematic due to issues of potentially changing market structures dueto financial deregulation and innovation, for example.)

Determining the size of the sample (the number of individual account)requires substantially more attention. How many depositor accountsshould be included in the sample? The answer in part depends on howaccurate the institution wants the forecast of the retention rate to be.The greater the desired accuracy, the larger the required sample ofaccounts. The answer also depends on the total pool of open accounts.The greater the number of accounts to sample from, the larger therequired sample as well, although the relation between number ofaccounts and required sample size is highly nonlinear. It is astraightforward exercise in statistics to demonstrate that theappropriate sample size is n=4k²s²/d² where n is the sample size, k isbased on the level of significance considered (typically 95% thusyielding a value of k of 1.96), s is the standard deviation of theunderlying population of deposit accounts, and d is the desired level ofaccuracy. (See Anderson, Sweeney and Williams, Statistics for Businessand Economics, (St. Paul: West Publishing, 1996), for example, for acomplete explanation underlying this equation.)

There are, however, three particular features about the process ofimplementing the formula that are not standard or straightforward instatistics. The first is the selection of a value for s, the standarddeviation of the underlying population of accounts. Before selecting thesample, s is unknown and hence an approximation must be input. Theprocess here assumes experience based values for s that vary dependingon the type of deposit. Assigning values employs information about thevariable ultimately to be forecasted, the retention rate. Consideringthe retention rate as a probability of retention, the process then is abinomial event in statistics. We then pick a conservative (i.e. low)estimate of the likely retention rate for the type of deposit. Forexample, for checking accounts, a yearly retention rate of 70 percentshould be considered conservative given prior applications. This valueimplies the appropriate value of s, which is used in the sample sizeequation.

The second feature is to pick a particular value of d. This componentdoes not have a single statistical requirement. The process lets thefinancial institution set this value although we normally recommend avalue for d in the range of 0.02 to 0.03. Lower values imply moreaccuracy and thus require a larger sample and higher costs. Thus, thechoice of the value of d is dependent on the institution's trade-off ofaccuracy versus cost.

The third feature of the sample size determination is based on therecognition that data collection costs must be weighed against thebenefits of improved accuracy. The above formula for n will yield asample size in all cases. However, the last step in determining thesample size is simply to check the costs associated with collecting thatsize sample with the benefits of the accuracy that such a sample sizewould imply. From a practical perspective, this feature generally capshand-collected sample sizes at 250-350 since larger samples generally donot yield appreciable improvements in forecast accuracy relative toincreased collection costs.

At this point, there is data for the financial institution on totalbalances 107, deposit rates 109, and survey balances by account 103, allfor alternate classes of deposits.

After collecting the survey data, the next step is to check the surveybalances for accuracy and for outliers 105. Since the forecasts forretention rates are potentially sensitive to outliers in the data andsince the financial institution may have provided hand-collected datasubject to errors, it is particularly advantageous to check foroutliers. The process for checking for outliers advantageously is twopart. Funds deposited in a non-maturity account may remain onlyovernight or for many years. When an account has a substantial temporaryincrease (or decrease) in deposits, however, one can reasonably questionwhether such a change is accurate or whether it has been mis-recorded.For example, in the transcription of account balances, it is possible tohave an account with actual balances of, say, $3,456 mis-recorded as$34,566. Alternately, it is possible that the same type of change couldbe due to a large transitory deposit, for example as a result of sellinga piece of property.

Such data entries are first reviewed with the institution to establishthe correct entry. In rare cases where the costs of reviewing the datapoints are too high, a method for resolving which of the two reasons isthe true cause underlying any particular outlying observation. Theprocedure adopted is that when either of two types of anomaliesdescribed above occurs, the result is presumed to be a transcriptionerror and the value is changed. The changes are: (1) When the old andnew numbers differ by a factor of approximately ten, as above with a“double”—in this case repeated 6—the “double” is presumed to be in errorand is removed. (2) When the old and new numbers differ in terms of thedecimal, e.g. $123.45 followed by $12,345., the decimal point ispresumed to have been inadvertently omitted. Otherwise, values are ispresumed to be correct. The second part of the general check foroutliers considers individual accounts rather than individualobservations. That is, an observation may be “influential” in terms ofbeing a single outlier for one account or an account itself may beunusual relative to the other accounts in the sample. Thus, a largeaccount may be excluded from the sample if it is atypical. The basicprocedure employed is that if in a sample of 250 accounts, for example,a single account makes up more than a certain percent of the deposits inthe sample, it would be deemed an influential account. (With 250accounts, the typical account would represent deposits of only 0.4percent of the sample deposits). This account would typically be deletedfrom the sample as unrepresentative of the accounts overall in thefinancial institution. Accounts with more than 5 percent of samplebalances are “flagged” and examined, while accounts of that certainpercent or more of sample balances typically are excluded. Ten percentis an appropriate percentage in the foregoing basic procedure, althoughother percentages will work.

This last adjustment is utilized so that the focus of the process is noton one or a few individual accounts in the survey but rather on thetotal balances of all accounts in the survey. If one account or a fewaccounts, in fact, were to dominate behavior for a deposit class at afinancial institution, then it would be inappropriate to delete theoffending account. Note that in all cases, accounts are deleted onlywith the understanding and acceptance of the institution.

Once the survey deposits have been checked, then the survey balances areaggregated for each account type and for each observation period toobtain the total survey balances by account type by period, referred tohereafter as survey balances 111. At this point, the data available bydeposit type and by month consists of the institution's total balances107, deposit rates 109, and survey balances 111. For furthercalculations, these variables are preferably in a spreadsheet 115 (e.g.,Excel or Lotus) and arranged, for example, with the columns indicatingthe variables and the rows indicating the appropriate months.

In addition to the variables internal to the institution, there are someexternal variables or exogenous variables 113 that also must be includedin the analysis and thus in the spreadsheet. Those variables includesome or all of four general types. The first are simply seasonal andday-of-the-month type variables, so-called binary or “dummy” variables(0/1 values). For example, each month (e.g. January) has a separateidentifying variable and each day of the week (e.g. for months ending ona Friday) also has a separate identifier. For example, a variable forFriday would take a value of 0 for all months that do not end on aFriday and would take a value of 1 for all months that end on Friday.The second external type of variable is Treasury interest rates. ThreeTreasury rates are included, for 90 day bills, for 1 year notes and for10 year bonds. These three adequately capture most features of the termstructure and the overall movement in general interest rate conditions.The third type of external variable is market deposit rates, that is,deposit rates for the typical institution in this financialinstitution's relevant market. Data may be gathered from a commerciallyavailable publication such as Bank Rate Monitor (BRM) or may be providedby the institution. These data need to be available for the same periodover which the institution's survey balances are available. Finally,additional local market condition descriptors may be entered as externalvariables. These are included to measure the health of the local orregional economy. These differ in availability across markets but ingeneral include the unemployment rate, personal income and retail sales.

The spreadsheet process 115 to this point simply puts the data in theappropriate format to begin the process of the statistical analysis thatleads to the forecasts. The spreadsheet is saved and the spreadsheetthen serves as an input, advantageously being incorporated directly intoa statistical package such as RATS (Regression Analysis of Time Series).

Part Two

Reference is made to FIG. 2. This part describes exemplary basicstatistical procedures employed to obtain equations that are used toforecast variables for the financial institution. The first step in thispart is to define some additional variables 203. Specifically, it isassumed that a financial institution's deposits (either total or survey)may be influenced either by the general level of interest rates or byinterest rate spreads. The relevant interest rate spreads potentiallyare of three types: differences between this institution's deposit ratesand those in the market, differences between this institution's rates ondifferent types of deposits, and differences between short-term andlong-term rates. All three types of spread variables are defined and arepotentially included in subsequent analysis although the exactdefinitions of the spreads are necessarily institution specific. One ormore of three types of spreads are included: (1) differences betweenshort-term and long-term rates, e.g. between the 90 day and 1 yearTreasury rates and between the 1 year and 10 year Treasury rates, (2)differences between this institution's rate on a particular depositcategory and that in its market, e.g. differences between thisinstitution's MMDA rate and the market (e.g., BRM) MMDA rate, and (3)differences between this institution's rates are different depositcategories, e.g., MMDA and NOW rates.

In addition to considering interest rate spreads, the process allows thepotential for institution-specific variables that cannot be picked up byeconomic variables as typically defined. For example, if an institutionhad a promotion on MMDA accounts from May to July giving free checkingif a minimum balance were maintained in an MMDA account, one mightsuspect that MMDA balances would increase in those months independent ofchanges in other variables such as interest rates. Thus it would beappropriate to define and include a specific binary variable thatassumed a value of 1 during the months of May through July and 0otherwise. The definition of institution-specific binary variables isdetermined based on information provided by the financial institutionand in consultation with management.

In 205, note that there are a total of four “blocks” of variables, theinstitution's total balances by account type 207, the institution'ssurvey balances by account type 209, the institution's deposit rates byaccount type 211 and other exogenous variables 213. The followinganalysis considers the disposition of variables, and makes somedistinctions on the basis of the different “blocks” of variables. Thefirst three blocks of variables are “explained” or related to variablesthat are either predetermined, that is, are available from priorobservation or from a prior period, or are exogenous, that is aredetermined outside the financial institution.

The process to explain these variables basically uses a modified versionof the standard statistical approach of regression analysis or ordinaryleast squares (OLS), again presented in a statistical text such asAnderson, et al., op. cit. or seemingly unrelated regression (SUR)presented in George G. Judge, William E. Griffiths, R. Carter Hill, andTsoung-Chao Lee, The Theory and Practice of Economics, (New York: Irwin,1980). With OLS, each variable of the financial institution (in thefirst three blocks) is sequentially related to lagged or predeterminedvariables. Thus, if there are a total of five variables in each of thethree blocks, there then would be a total of 15 equations estimated withOLS (or SUR). The OLS procedure involves relating a variable at a pointin time t, defined as Y_(t), e.g. checking account balances, to priorvalues of this variable, denoted Y_(t-L), as well as to prior values—andthus known values—of variables in the other three blocks. These could bedenoted as Y2 _(t-L). In addition, Y_(t) also is potentially related tocurrent and to lagged values of the exogenous variables, labeledX_(t-L). Thus, one could consider the equation:Y _(t)=α₀+α₁ Y _(t-L)+α₂ Y2_(t-L)+α₃ X _(t-L)  (1)where

-   -   X=exogenous variable,    -   Y=variable,    -   t=time,    -   L=lag time,        and where the values for the parameter α_(i)'s are obtained by        regression using a statistical package such as RATS.

In practice, it would be inappropriate to estimate a single equation inisolation. That is, the behavior of checking account balances is likelynot independent of the behavior of savings account balances or perhapssavings account deposit rates. Thus, the process here considers a systemof equations such as (1), one equation for each category of coredeposits to be forecasted. A general system of equations such as (1),when estimated together, is typically called vector autoregressive (VAR)analysis. VAR analysis is a relatively recent introduction in thehistory of statistics, and its application to forecasting has beengrowing dramatically. (For example, see Hafer and Sheehan, “TheSensitivity of VAR Forecasts to Alternative Lag Structures,”International Journal of Forecasting 5 (1989), pp. 399-408 and Robertsonand Tallman, “Vector Autoregressions: Forecasting and Reality,” EconomicReview, Federal Reserve Bank of Atlanta, (First Quarter, 1999), pp.4-18.) VAR procedures have been shown to yield relatively accurateforecasts in a wide range of applications. However, as both thesecitations note, the application of VAR estimation requires a number ofassumptions and those assumptions may critically influence theestimation and forecasting powers of the model. The exemplary process ofspecifying those assumptions or criteria are spelled out in thefollowing paragraphs in a broad sense. In a number of cases, however,there are reasonable alternatives that are allowable and that areincluded the process here. Those alternatives are more fully describedin Part Three.

The general estimation process 217 adopted here is called VAR analysis.The preferred approach is called subset VAR analysis and has beenpreviously employed in Sheehan, “U.S. Influences on Foreign MonetaryPolicy,” Journal of Money, Credit and Banking, 24 (November 1992), pp.447-64. The logic underlying the use of subset VAR analysis is simple.In a typical application of the process described here, there could befive types of assets, thus 15 endogenous variables—five total balancevariables, five survey balance variables and five deposit ratevariables. In addition, there typically are over 20 exogenous variablesthat potentially belong in each estimated equation. If each variable isallowed to enter with only two lags (L=2 in the notation of equation(1)), that would imply a total of 35 different variables with two lagseach for a possible total of 70 right-hand side variables. Given thatthe additional right-hand-side variables in (1) require additional datato obtain reasonably accurate estimates of the parameters or the α₁'s in(1)—econometricians would say that each additional variable uses adegree of freedom—the required data sample would have to besubstantially longer than 70 periods long. Using monthly data, thatwould mean a period longer much than six years. However, there is noguarantee that a financial institution would face the same marketstructure, which appears an unreasonable assumption over a ten or twentyyear period given the history of merger activity and financialinnovation and deregulation. Thus, a subset VAR is very helpful toreduce the dimensionality of the problem. However, creating a subset VARnecessary entails substantial additional assumptions.

The first part of reducing the dimensionality of the VAR is to determinethe criteria whereby variables are to be included or excluded: lagselection criteria 219. A number of statistical criteria are availableas described in Hafer and Sheehan, op. cit. The basic criterionpreferably employed here is the Bayesian Information Criterion (BIC)which has the property that the selection of variables included is thetheoretically correct choice at least asymptotically. (The processallows other criteria to be chosen and that will be discussed below.)Thus, whether a variable is included or excluded from (1) is based onthe results of a statistical criterion such as the BIC.

There also is a question of the appropriate lag length, left unspecifiedin the general context of equation (1). There is no theoreticaldetermination possible of the appropriate lag length, although much hasbeen written on the subject. Here, the approach is to specify themaximum lag length allowed, following Hafer and Sheehan, and then havethe BIC criterion determine which of the lags are, in fact, appropriate.The maximum lag length is left open but with monthly data therecommended lag length is two months in most applications. Again, thisassumption reduces the dimensionality of the problem and is required bythe sample size.

The additional assumptions employed in the VAR order of estimationprocess 215 are straightforward. There are a total of four blocks ofvariables as noted above 205, three within the institution and oneexogenous. The process constrains relations between the blocks. Theblocks can be labeled T for the vector of variables included in totalbalances, S for the vector of survey balance variables, R for the vectorof deposit rates, and X for the vector of exogenous variables. Thevector X is assumed to be determined independent of any considerationsin the other three vectors. That is, the financial institution does nothave any impact on market rates such as Treasury bill rates. The vectorS for survey balances is assumed to be potentially influenced by depositrates but not by total balances. That is, whether an account remainswith the institution may depend on the institution's rates but does notdepend at least directly on the institution's total deposit balances.The vector T is assumed to be potentially influenced both by depositrates and by survey balances (and thus retention rates). And the vectorR potentially influences both survey and total balances and ispotentially influenced by those in turn. That is, the institution maychange deposit rates either in response to changing retention rates orin response to changes in total balances. (The statistical properties ofthe T, S and R vectors require that changes in T and S influence thelevels of R since R typically is an I(0) series while T and S typicallyare I(1) series. See James D. Hamilton, Time Series Analysis (Princeton,N.J., Princeton University Press, 1994) for a complete discussion of themeaning and differences between I(0) and I(1) series).

At the end of Part Two, the process yields the basic estimationequations or estimate regressions 221 based on a subset VAR model thatare employed to forecast retention rates in particular but alsopotentially deposit rates and total balances. Before moving to theforecasting approach, however, it is important to note in this partthere was some discussion of potential alternatives that are allowed andthere is some flexibility in the estimation process. Part Three goesthrough alternatives in much more detail, in particular, alternativesthat further distinguish this approach from any others employedpreviously.

Part Three

The prior section describes the basic approach. Within this approach,however, there is substantial flexibility. This section describes fouradditional areas where alternatives to the standard approach are allowedthat potentially generate much improved forecast accuracy or that implysubstantially better explanations for why retention rates change, forexample.

First, as mentioned in the prior section, there are a number ofstatistical criteria that could be employed as the basis for choosinglag lengths and included variables. The standard employed here is theBIC. The advantage of that criterion is that it generates asymptoticallycorrect results. The limitation, however, is that in very small samplesit may include too few variables.

Reference is made to FIG. 3. Thus, the financial institution is affordedthe alternative 301 of alternative selection criteria 303 such as theFinal Prediction Error (FPE) criterion. These additional criteria arepresented and discussed in Hafer and Sheehan, op. cit., and theirforecasting performance in a macroeconomic setting are discussed indetail there. If an institution wanted to ensure that there were novariables that were falsely excluded from the estimated equation, thenthe FPE would be a reasonable alternative to the BIC. The cost of such achange, however, would be to potentially include in the equationvariables that in fact should not be included.

Second, the typical regression and the typical VAR are linear both inthe estimated parameters and in the choice of variables. While OLSrequires linearity in the estimated parameters, it does not requirelinearity in the choice of variables. In the event that a linear systemof equations is not satisfactory 305, there are nonlinear optionsoffered 307. The first allows variables to be included either in linearform (the standard) or in logarithmic form. The advantage to using logsis simply that the estimated coefficients, the α₁'s in (1) are theninterpreted as the estimated elasticities. Thus, this approach yields aquick answer to questions like: if deposit rates rise by 5 percent, whatwould be the resulting percent change in the level of total deposits?The second nonlinearity allowed considers asymmetric response. That is,when considering the impact of interest rate changes, for example, todate all forecasting models of deposits or retention rates assume thatrate increases and decreases have symmetric impacts. Here, thepossibility of asymmetric response is allowed with the option ofallowing rate increases and decreases to have different impacts on totalbalances and survey balances.

Third, many economic variables have trends, and total balances atfinancial institutions are typical in this regard. That is, most healthyfinancial institutions have trend increases in many if not most depositcategories. The typical regression and VAR estimated to date hasemployed a simple time trend to capture this effect. (That is, avariable t would be defined as having a value of 1 in the first period,2 in the second, 3 in the third, etc. and this variable would beincluded in the list of exogenous variables.) While this approach workswell in many cases, it is limited in that it assumes that there is butone trend over the entire period. For example, if the estimation periodruns from 1995:1 through 1999:12, including a simple trend would requirethe same change in deposits for each period over this interval. Theprocess here employs a generalization of this approach and, if the trendterms are not satisfactory 309, allows both multiple trends and splittrends 311, with the choice of trends again based on a statisticalcriterion like the BIC. A final system of equations is produced 317.

Fourth, while the notation and discussion has referred consistently todeposit rates and deposit balances, the process may be extended also toassets 313. Thus, deposits and loans (or bonds) can be examined in ananalogous manner 315. This utilizes two modifications to the abovediscussion. One is the explicit consideration of three additionalblocks, one for total assets (A), one for survey assets (B), and one forthe interest rates on those assets (C); the other is to consider theimplications of levels versus the changes in those assets. On theadditional blocks, total assets are allowed to influence asset rates butnot survey assets; survey assets may influence both asset rates andtotal assets; and asset rates may influence both total assets and surveyassets. In addition, asset rates may influence deposit rates andvice-versa while survey assets do not influence survey deposits (or thereverse) at least directly and generally total assets do not influencetotal deposits (or the reverse) again at least directly. The first setof restrictions are identical to those for deposits. The only additionalconsideration when dealing with assets rather than deposits concerns atechnical issue of examining levels versus rates of change. Whenconsidering survey deposits, the analysis considers the level ofdeposits as a prelude to calculating the retention rate of surveydeposit balances rather than focusing on the rate of change. Whenconsidering survey assets, for example, the outstanding survey balancesof VISA cards, there is a question of whether it is more appropriate toconsider the level of VISA balances or the change in the amount of thosebalances, that is, the amount paid off each month. Consistent with theapproach to deposits, the process focuses on the level rather than therate of change. The forecasting procedure, however, is robust enough togenerate forecasts of balance payments if that was of interest to thefinancial institution. This modification also allows a breakdown ofdeposit categories into generally separate blocks, e.g., personal vs.business, where personal would refer to the vectors T, S and R mentionedearlier and business would refer to the vectors A, B and C. Thus, thethree basic “building blocks” can be repeated and joined together asnecessary, multiple times as necessary.

Part Four

Reference is made to FIG. 4. The forecasting itself is based on thesimultaneously estimated system of equations 317 from a subset VAR andtheir repeated use. That is, there are a system of equations such as (1)above, each explaining a single variable in one of the vectors for totalbalances, survey balances or deposit rates. Considering a simpletwo-variable and one lag analog, the equation system could be writtenas:Y _(t)=β₀+β₁ Y _(t-1)+β₂ X _(t-1)andX _(t)=δ₀+δ₁ X _(t-l)+δ₂ Y _(t-l).  (2)where

-   -   Y=first endogenous variable,    -   X=second endogenous variable,    -   t=time.        and where the β's and δ's again are parameters obtained by        regression.

These two equations can be used to forecast Y and X as far into thefuture as desired. That is, knowing the values or having forecasted thevalues of Y₀ and X₀, forecasts of Y₁ and X₁ can be obtained and theseforecasts can then be employed to generate forecasts of Y₂, X₂, Y₃, X₃,. . . This process serves as the basis for the forecasting approachemployed here and this “bootstrapping” approach is employed whenever VARanalysis is employed for forecasting 401.

While this basic approach is well known, there are a number of specificassumptions that are made to implement the forecast process.

The first assumption concerns the treatment of the so-called external(exogenous) variables. That is, some variables such as market interestrates and Treasury interest rates are taken as given by the financialinstitution. However, to implement the forecasting process as describedby (2) above, it is necessary to have future values (or forecasts) forthese variables as well. Generating those forecasts is two part.Treasury rates are forecast first. The standard initial “forecast” is tosimply assume they will remain unchanged. However, the process allowsthe institution to define specific hypothetical changes or to forecastTreasury rates also using a VAR model. For other exogenous variables,for example, local market interest rates, they are related (regressed)on Treasury rates and their own lags again using a VAR and the BICincluding a maximum of two lags (although all those specifications canbe modified in conjunction with the discussion in Part Three). Theresulting equations together with the Treasury rate forecasts areemployed to forecast these variables as far into the future as desired,again employing the process described by (2) above.

The second assumption concerns the forecast horizon. There is notheoretically “correct” forecast horizon. From the financialinstitution's perspective, the appropriate question is what is theapplication of the forecast? The answer to that question normallydetermines the appropriate horizon. To allow the forecasts generatedhere to be employed in a wide range of advantageous applications, theprocess allows the institution to specify two different horizons. One isa monthly horizon; for how many individual months in the future does theinstitution want monthly forecasts? The other is a yearly forecast; thatis, how far into the future does the institution want end-of-year valueforecasts? The procedure is general and allows virtually any forecasthorizon. However, the standard horizons chosen tend to be one or twoyears of monthly forecasts and 15 to 20 years of yearly forecasts.

These two assumptions are sufficient to yield a “base” forecast 403.That is, given constant Treasury rates, the process determines what willhappen to total deposits, survey deposits and deposit rates over theinstitution-defined horizon. In addition, the forecasts of surveydeposits are used to calculate so-called retention rates. Retentionrates are the calculated ratio of forecasted survey balances in somefuture period t+k relative to survey balances in the most recent periodt. This ratio is a key input into determining the value of accountbalances as described in the subsequent section.

Beyond these two assumptions, however, the process also allows thefinancial institution three additional choices 405. The first relates toan option to specify alternatives to the “base” forecast, e.g., toconsider what happens in cases where interest rates do not remainconstant. Specifically, regulators of financial institutions as well asthe institutions themselves typically are concerned with what willhappen in periods of changing interest rates. One of the weaknesses ofmost prior models of retention rates, for example, is that they do notallow changing interest rates to have any impact on retention rates,although clearly they could have a major impact. Thus, it is importantto have forecasts for other rate assumptions beyond the base case, todemonstrate any rate related behavior sensitivity.

The process allows three different approaches to the generation of thoseadditional forecasts based on different patterns of Treasury ratebehaviors 407. The first is what is referred to as the standardregulatory approach. That is, Treasury rates are increased or decreasedby a fixed amount, e.g. 100, 200 or 300 basis points, and then theestimated equations are employed using as inputs those higher or lowerTreasury rates. This approach is called the standard regulatory approachbecause it follows the approach typically employed by regulators isassessing interest rate risk of assuming that rates increase (ordecrease) immediately by a given amount and then remain at their higher(or lower) values for the indefinite future. The second approach togenerating these additional forecasts assumes instead that Treasuryrates increase as in the first approach by some fixed amount but do itover a user-defined interval. That is, rather than assuming thatinterest rates increase immediately by 100 basis points, it would allowinterest rates to increase over the next year by 100 basis points. Thisapproach is labeled the Ramp approach or forecast. The third approach togenerating these additional forecasts allows user-defined changes inTreasury rates, and then calculates how other variables change asdescribed above.

The second choice allowed is to determine what variables—or what blocksof variables—will be allowed to vary in the forecast 409. The base caseallows all variables to vary freely depending on the specifiedequations. There are provided at least two alternatives to this fullmodel forecast 411, 413. The first alternative is called “balancesconstant 413.” In this case, all total balances are constrained toremain constant at their last observed value. The focus in this casetypically is on the deposit rates with the question of how do depositrates have to change with a given change in Treasury (and thus market)rates in order to maintain deposit balances. The other alternative isanalogous and is called “rates constant 411.” Here, deposit rates areconstrained to remain constant at their last observed value. In thisscenario the focus typically is on what would happen to deposit balancesif the financial institution did not alter rates, especially in the faceof changing market rates.

The third choice allowed considers the type of forecast generated,dynamic or steady-state 417. The base case considers the dynamicforecast and simply uses the most recent values, i.e. those available attime 0, to forecast the next period values, say at time 1, which are inturn used to forecast values in the subsequent period. The advantage tothis approach is that it yields real-time forecasts based on the actualvalues and the history of the variables being forecast. Thedisadvantage, however, is that in some cases it may be sensitive tooutliers or unusual observations in the last period or two of thesample. That is, if in the last observation period there was a dramaticdecrease in checking account balances, for example, the forecasts basedon that may view that decrease as a permanent change and may extrapolatethat into continuing decreases in the future. (This situation is not acommon outcome, but cannot be ruled out on theoretical grounds anddepends on other statistical properties of the estimation process,specifically, is the dependent variable a random walk or close to arandom walk.) Thus, a check on the process is to calculate thesteady-state or long-run forecast values as well. That is, consideringequation (2) above, if Y were constant over time, what would it imply?Other things equal, then Y_(t)=Y_(t-1) and the first of the tworelations can be solved for Y:Y=(β₀+β₂ X _(t-1))/(1-β₁).  (3)where

-   -   X=exogenous variable    -   Y=variable    -   β=potential parameters

This would be the steady state value of Y. Clearly as other variables inthe X vector change over time, e.g. as Treasury rates change, theequilibrium value of Y also would change. However, Y would no longer bedependent on its own history in terms of the solution procedure for theforecasting approach. Thus, the equilibrium or steady state forecast canbe calculated 419. This approach to forecasting is viewed as asupplement to the basic dynamic approach to forecasting typicallyemployed both here and elsewhere.

Part Five

Once the forecasts have been generated, they are loaded into aconventional spreadsheet in the usual manner for further analysis, inparticular, for use in calculating base case (no change in Treasuryrates) and alternate rate scenario estimates of behavior and the valueof deposits. Reference is made to FIG. 5, illustrating the entireprocess beginning with data assembly (501 to 511), basic estimation (513to 519), forecasting (521-523), and production (525-543). Steps 501 to523 are discussed in more detail below.

At step 501, institutional needs are identified. At step 503, dataavailability is identified. At step 505, time series and categories areidentified. At step 507, core deposit and CD data are collected. At step509, historic reviews are produced. At step 511, final data qualityassurance is performed.

Preliminary statistical testing is performed at step 513, and multi-stepeconometric estimations are performed at step 515. A quality analysis ofinitial equation system is done at step 517, and at step 519, finaleconometric estimations are done. At step 521, forecast estimates areproduced. At step 523, data is input to application systems. At step525, the system produces specific applications.

Steps 527 to 531 concern the total balances application, which considersbaseline trend data, rate sensitivity data, and liquidity needs. At step529, a base case (no change in future interest rates) forecast of totalbalances is produced first, using the system of simultaneous equationsfrom the econometric estimations. The forecast, normally done for 24individual future month end periods, provides insights into the baselinetotal balances “momentum” in a deposit category—Is it flat (no change),increasing, or decreasing? This assists managers in quantitativelydetermining funding and liquidity needs if interest rates stay generallyconstant.

At step 531, forecasts of total balances by time period are alsoconducted for hypothetical situations where interest rates rise ordecline in the future (multiple choices of specific future interest ratepaths can be accommodated). Indicated changes in the supply of categorytotal balances across interest rate scenarios provide managers withmeasurements of the supply elasticity of category total balances (uponwhich pricing decisions can be based) and liquidity management insights.

In the alternate interest rate scenario forecast, total balances ofother deposit categories, category own rate paid (if a rate bearingcategory), own rates paid on other categories, competitor rates paid,and all other forecast influences are adjusted along with the definedinterest rate changes. Thus multiple influences contribute to futureforecast values that are fully comprehensive and simultaneouslydetermined by all relevant factors.

Steps 533 to 537 concern the rates paid applications, which take intoconsideration the optimal rate paid, repricing paths, and Betacoefficients. At step 535, a base case (no change in future interestrates) forecast of the institution's own rate paid is produced first,using the system of simultaneous equations from the econometricestimations. The forecast, normally done for 24 individual future monthend periods and for annual year end periods out to 20 years, providesestimates of the institution's expected rates paid if historic pricingbehaviors were applied to current interest rate levels. Current ratepaid may be equal to, above (rich to history) or below (cheap tohistory) the estimated future rate paid. Knowing this relationshipassists managers in setting optional rates paid at step 537 and thus inoptimally managing interest expense.

Forecasts of own rate paid by time period are also conducted forhypothetical situations where interest rates rise or decline in thefuture (multiple choices of specific future interest rare paths can beaccommodated). Indicated changes in category own rate paid acrossinterest rate scenarios provide managers with measurements of thehistoric repricing behavior of the category. This offers guidance inrepricing decisions and is the source for quantified beta (repricingspeed) coefficients and specific repricing lag matrix inputs in ALM(asset-liability management) models.

In the alternate interest rate scenario forecasts, category own ratepaid (if a rate bearing category), own rates paid on other categories,total balances of other deposit categories, competitor rates paid, andall other forecast influences are adjusted along with the definedinterest rate changes. Thus multiple influences contribute to futureforecast values that are fully comprehensive and simultaneouslydetermined by all relevant factors.

Steps 539 to 543 concern the retained balances applications, in whichaverage lives and sensitivity to rate environments are considered. Atstep 539, a base case (no change in future interest rates) forecast ofthe institution's retention of existing balances is produced first,using the system of simultaneous equations from the econometricestimations. The forecast, normally done for 24 individual future monthend periods and for annual year end period values out to 20 years,provides estimates of the category's expected retained balancesbehaviors if historic tendencies are projected at current interest ratelevels. This provides quantitative insights into the baseline retention“momentum” in a deposit category—Is it flat (no change), decreasing, or(in some cases) increasing? This assists managers in quantitativelycalculating run off patterns (run off being the difference in retentionfrom period to period). The run off data are used in the calculation ofaverage lives, present values, and premiums (book value-present value),step 543.

Forecasts of retained balances behaviors by time period are alsoconducted for hypothetical situations where interest rates rise ordecline in the future (multiple choices of specific future interest ratepaths can be accommodated). Indicated changes in retained balancebehaviors across interest rate scenarios provide managers with specificmeasurements of the rate sensitivity of retention behavior. Thisinformation is the source for quantifying category average lives,present values, premiums, and associated inputs for use, e.g., in ALMmodels. The indicated changes in category average lives, etc., asinterest rates vary (i.e., their sensitivity to rate changes) provides aquantified measure of the convexity of the category's value.

In the alternate interest rate scenario forecast, retained balances ofother categories, own category rate paid (if a rate bearing category),own rates paid on other categories, total balances of other depositcategories, competitor rates paid, and all other forecast influences areadjusted along with the defined interest rate changes. Thus multipleinfluences contribute to future forecast values that are fullycomprehensive and simultaneously determined by all relevant factors.

The invention may also be applied to other financial assets orliabilities that are characterized by indeterminate behavior. Thesefinancial assets include, for example, CD's, VISA balances outstanding,international funding categories, etc.

The most highly preferred embodiment of the invention is in connectionwith core deposits. Nevertheless, the invention encompasses financialassets and financial liabilities, and is intended to reach any form offinancial instruments.

While the preferred mode and best mode for carrying out the inventionhave been described, those familiar with the art to which this inventionrelates will appreciate that various alternative designs and embodimentsfor practicing the invention are possible, and will fall within thescope of the following claims.

1. A method for determining a useful life of balance sheet items,comprising the steps of: (A) receiving data for each of a plurality ofbalance sheet items, the data including a sample of account balances, asize of the sample being n=4k²s²/d² wherein s is an estimated yearlyretention rate, d is in the range of 0.01 to 0.03 and k corresponds to alevel of significance; (B) performing, in a computerized system, adynamic calculation of a first retention rate for each of a plurality ofbalance sheet items using the data received in step (A); (C) performing,in the computerized system, a steady-state calculation of a secondretention rate for the plurality of balance sheet items using the datareceived in step (A); (D) combining said first and second retention rateto determine a predicted useful life of the combined plurality ofbalance sheet items; and (E) outputting the predicted useful life. 2.The method of claim 1, further comprising the step of selecting one of aplurality of variables affecting at least one of the retention rates. 3.The method of claim 2, further comprising the step of determining asensitivity of balance sheet item variables to other deposit variables.4. The method of claim 1, further comprising the step of forecastingscenarios extrapolated from said retention rate.
 5. The method of claim1, wherein the data for each of the plurality of deposits includes totaldeposit balances, deposit rates, and a sample of account balances. 6.The method of claim 1, wherein a length of the sample is four years. 7.The method of claim 1, wherein k is 1.96.
 8. The method of claim 1,further comprising the step of checking for outliers in the plurality ofbalance sheet items.
 9. The method of claim 1, further comprising thestep of including exogenous variables in at least one of thecalculations.
 10. The method of claim 9, wherein the exogenous variablesare selected from the set of seasonal variables, day-of-the-monthvariables, treasury interest rates, interest rates, local unemploymentrate, local personal income, and local retail sales.
 11. The method ofclaim 1, further comprising the step of including interest rate spreadin at least one of the calculations.
 12. The method of claim 3, whereinthe step of forecasting scenarios includes providing future values foruse in at least one of the calculations.
 13. The method of claim 12,wherein the future values are selected from the set of forecast treasuryrates, forecast horizon, forecast deposits, forecast retention rates,and forecast interest rates.
 14. The method for determining a usefullife of balance sheet items comprising the steps of: (A) performing, ina computerized system, a dynamic calculation of a first retention ratefor each of the plurality of balance sheet items; (B) performing, in thecomputerized system, a stead-state calculation of a second retentionrate for the plurality of balance sheet items; (C) combining said firstand second retention rate to determine a predicted useful life of thecombined plurality of balance sheet items; (D) selecting one of aplurality of variables affecting at least one of the retention rates;(E) determining a sensitivity of the selected variable to other balancesheet item variables; (F) forecasting scenarios extrapolated from saidretention rate, wherein the step of forecasting scenarios includesproviding future values for use in at least one of the calculations, andwherein the future values are selected from the set of forecast treasuryrates, forecast horizon, forecast balance sheet items, forecastretention rates, and forecast interest rates; (G) wherein the balancesheet items include deposits and financial instruments; (H) wherein thedata for each of the plurality of financial assets includes totalbalances, interest rates, and a sample of account balances, wherein alength of the sample is four years, wherein a size of a sample isn=4k²s²/d², and wherein s is an estimated yearly retention rate, d is inthe range of 0.01 to 0.03, and k corresponds to a level of significance;(I) checking for outliers in the plurality of balance sheet items; (J)including exogenous variables in at least one of the calculations,wherein the exogenous variables are selected from the set of seasonalvariables, day-of-the-month variables, treasury interest rates, interestrates, local unemployment rate, local personal income, and local retailsales; (K) including interest rate spread in at least one of thecalculations; and (L) outputting the predicted useful life of thecombined plurality of balance sheet items.
 15. A computerized system fordetermining a useful life of balance sheet items, comprising: (A)receiving means for receiving data for each of a plurality of balancesheet items, the data including a sample of account balances, a size ofthe sample being n=4k²s²/d² wherein s is an estimated yearly retentionrate, d is in the range of 0.01 to 0.03 and k corresponds to a level ofsignificance; (B) means for dynamically calculating a first retentionrate for each of the plurality of balance sheet items using the datareceived by the receiving means; (C) means for calculating asteady-state second retention rate for the plurality of balance sheetitems using the data receiving by the receiving means; (D) means forcombining the first and second retention rates to determine a predicteduseful life of the combined plurality of balance sheet items; and meansfor outputting the predicted useful life.
 16. The system of claim 15,wherein at least one of the retention rates is affected by one of aplurality of balance sheet item variables.
 17. The system of claim 16,further comprising a means for determining a sensitivity of one of thebalance sheet item variables to other balance sheet item variables. 18.The system of claim 15, further comprising means for extrapolating aforecast scenario from said retention rate.
 19. The system of claim 15,wherein the balance sheet items include financial instruments.
 20. Thesystem of claim 15, wherein the data for each of a plurality of balancesheet items includes total balances, interest rates, and a sample ofaccount balances.
 21. The system of claim 15, wherein a length of thesample is four years.
 22. The system of claim 15, further comprisingmeans for identifying outliers in the plurality of balance sheet items.23. The system of claim 15, wherein exogenous variables are included inat least one of the calculations.
 24. The system of claim 23, whereinthe exogenous variables are selected from the set of seasonal variables,day-of-the-month variables, treasury rates, interest rates, localunemployment rate, local personal incomes, and local retail sales. 25.The system of claim 15, wherein an interest rate spread is included inat least one of the calculations.
 26. The system of claim 17, whereinthe forecast scenario is based on a future value for use in at least oneof the calculations.
 27. The system of claim 26, wherein the futurevalues are selected from the set of forecast treasury rates, forecasthorizon, forecast balance sheet items, forecast retention rates, andforecast interest rates.
 28. The system of claim 15, comprising adisplay of the predicted useful life of the combined plurality ofbalance sheet items.
 29. A computerized system for determining a usefullife of balance sheet items, comprising: (A) means for dynamicallycalculating a first retention rate for each of a plurality of balancesheet items; (B) a steady-state means for calculating second a retentionrate for the plurality of balance sheet items; (C) means for combiningthe first and second retention rates, to determine a predicted usefullife of the combined plurality of balance sheet items; (D) means fordetermining a sensitivity of a balance sheet item variable that affectsat least one of the retention rates to other balance sheet itemvariables; (E) means for extrapolating a forecast scenario from saidretention rate, wherein the forecast scenario includes future values foruse in at least one of the calculations, and wherein the future valuesare selected from the set of forecast treasury rates, forecast horizon,forecast deposits, forecast retention rates, and forecast interestrates; and (F) means for outputting the predicted useful life of thecombined plurality of financial assets; (G) wherein the data for each ofthe plurality of balance sheet items used for calculating the first andsecond retention rates includes total balances, interest rates, and asample of account balances, wherein a length of the sample is fouryears, wherein a size of a sample is n=4k²s²/d², and wherein s is anestimated yearly retention rate, d is in the range of 0.01 to 0.03, andk corresponds to a level of significance; (H) wherein outliers areidentified in the plurality of financial assets; (I) wherein exogenousvariables are included in at least one of the calculations, theexogenous variables being selected from the set of seasonal variables,day-of-the-month variables, treasury rates, interest rates, localunemployment rate, local personal income, and local retail sales; and(J) wherein an interest rate spread is included in at least one of thecalculations.
 30. The method of claim 14, wherein k is 1.96.
 31. Thesystem of claim 15, wherein {acute over (k)} is 1.96.
 32. Thecomputerized system of claim 29, wherein k is 1.96.
 33. The method ofclaim 1, wherein the balance sheet items comprise financial assets andfinancial liabilities.